The flight instructor reported that he had successfully completed the demonstration of several flight maneuvers for the student pilot. He configured the helicopter for a hovering autorotation, closed the throttle, and the helicopter subsequently descended in a left skid low attitude. The left skid of the helicopter struck the ground, and the instructor attempted to apply corrective control inputs. The helicopter then rolled onto its left side, causing substantial damage to the fuselage and the main rotor system. The flight instructor reported that the helicopter and engine had no mechanical failures or malfunctions prior to the accident. He further stated that the accident could have been prevented if he applied right cyclic, and right yaw pedal control during the descent, and cushioned the landing by raising the collective control.